This is from an older (~2009) version of the books. Chapter 5, #49. Passage describes a generic standing wave on a string and Figure I is just a diagram of the wave.
#49: At a particular time, the amplitude of the vibrating string in Figure I is zero. What can be said about the energy of the standing wave at this point?
A. The energy of the wave is zero.
B. The wave has only kinetic energy.
C. The wave has only potential energy.
D. The wave has both potential energy and kinetic energy.
At a node, there is no kinetic energy intuitively because that point on the string doesn't move. Mathematically, it also seems like the energy at nodes is zero for all t: http://arxiv.org/pdf/1007.3962.pdf (page 4, halfway down). But TBR's solutions claim the answer is B because of a harmonic oscillator analogy. That seems reasonable for an anti-node, but I'm not sure how it applies to nodes.
#49: At a particular time, the amplitude of the vibrating string in Figure I is zero. What can be said about the energy of the standing wave at this point?
A. The energy of the wave is zero.
B. The wave has only kinetic energy.
C. The wave has only potential energy.
D. The wave has both potential energy and kinetic energy.
At a node, there is no kinetic energy intuitively because that point on the string doesn't move. Mathematically, it also seems like the energy at nodes is zero for all t: http://arxiv.org/pdf/1007.3962.pdf (page 4, halfway down). But TBR's solutions claim the answer is B because of a harmonic oscillator analogy. That seems reasonable for an anti-node, but I'm not sure how it applies to nodes.